Hypothetico-Deductive Method

1. Hypothetico-Deductive Method Lars-G�ran Johansson Filosofiska Institutionen Uppsala Universitet Hypothetico-Deductive Method Lars-G�ran Johansson 1

2. Hypothetico-Deductive Method Hypothetico-Deductive Method Lars-G�ran Johansson 2 �We and other animals notice what goes on around us. This helps us by suggesting what we might expect and even how to prevent it, and thus fosters survival. However, the expedient works only imperfectly. There are surprises, and they are unsettling. How can we tell when we are right? We are faced with the problem of error.� (W.V. O Quine) .

3. Hypothetico-Deductive Method Scientists, in all disciplins, formulate and test hypotheses The test outcome is either that the hypothesis is confirmed or disconformed No singular hypothesis can ever be definitely falsified or proved. Testing is not meaningful if you are not prepared to reject the hypthesis! Hypothetico-Deductive Method Lars-G�ran Johansson 3

4. Francesco Redi (1668): �I began to think that worms found in meat came from flies and not from rottening. I was convinced when observing that flies were flying around the meat before it was full of worms. Beliefs not corroborated by experiment are worthless. Therefore I put a dead snake, pieces of fish and a slice of veal in four big jars with wide openings, which I covered and sealed. Then I filled another four jars with the same stuff but left these open. Flies were repeatedly seen passing in and out in the open jars and the meat in those were full of worms. But the covered jars contained no worms, even though the meat was rotten. Hence, meat from dead animals cannot generate worms without egg from living creatures are put in it.� Hypothetico-Deductive Method Lars-G�ran Johansson 4

5. Structure of argument Hypothesis: Worms are spontaneously generated in rottening meat. Empirical Consequence: If rottening meat is kept in a covered jar, worms will be seen in the jar after some time. Premiss 1: If H, then E Premiss 2: E false ____________________ Conclusion: H false Hypothetico-Deductive Method Lars-G�ran Johansson 5

6. Continued Auxiliary Assumption: Covering a jar with waxed paper does not affect the self generating process. If (H and A), then E E false _________ H or A false Hypothetico-Deductive Method Lars-G�ran Johansson 6

7. Continued �Since the air could not circulate in the covered jars, I performed a new experiment in order to exclude all doubts. I put meat and fish in a beaker which I covered with gauze. In order to further protect it from flies I put the beaker in a cage of gauze. I saw no worms in the meat, in spite of many worms outside the cage and flies all the time landed on the cage and put their worms there.� Hypothetico-Deductive Method Lars-G�ran Johansson 7

8. Radiation laws First attempt by Planck: Hypotheses: Matter consists of atoms behaving as harmonic oscillators All available energy states are equally probable at thermal equilibrium Matter emits and absorbs energy as classical oscillators Hypothetico-Deductive Method Lars-G�ran Johansson 8

9. Radiation laws Hypothetico-Deductive Method Lars-G�ran Johansson 9

10. Radiation laws Second attempt Hypotheses: Matter consists of atoms behaving as harmonic oscillators All available energy states are equally probable at thermal equilibrium Matter emits and absorbs energy in discrete portions Hypothetico-Deductive Method Lars-G�ran Johansson 10

11. Radiation laws Now the derived function is Hypothetico-Deductive Method Lars-G�ran Johansson 11

12. Logical analysis Premiss 1: If (H1, H2 and H3) then Planck�s law Premiss 2: Planck�s law gives correct predictions Conclusion: Hypotheses supported. N.b! H1: Matter consisting of atoms taken for granted. H2: Equipartition principle taken for granted. Hence, H3 is the tested hypothesis! Hypothetico-Deductive Method Lars-G�ran Johansson 12

13. Emile Durkheim (1858-1917): De la Suicide H: The incidence of suicide is higher in societies with a lower degree of integration than in those with a higher degree. A1:Catholic societies are more integrated than protestant ones,if other aspects are similar. A2: Swiss cantons are socially similar, except form of religion E:Catholic cantons have a lower suicide incidence than protestant ones. Hypothetico-Deductive Method Lars-G�ran Johansson 13

14. Observations Type of society: suicide/miljon inh. Catholic cantons 86,7 Mixed 212,0 Protestant cantons 326,3 Hypothetico-Deductive Method Lars-G�ran Johansson 14

15. Claude Bernard (1813- 1878) Found that the following generalisations hold: Carnivores have acid and clear urine Herbivores have alkaline and muddy urine But A number of newly arrived rabbits had acid and clear urine! Hypothesis needed! Hypothetico-Deductive Method Lars-G�ran Johansson 15

16. Testing of hypothesis H: Hypothesis: They had been starving and thereby metabolised their own meat. E1: Giving the rabbits grass will result in normal alkalic urine E2: Dissection will show that the rabbits have metabolised their own meat E3: If horses are starved they too will get acid and clear urine If H & T, then E1, E2 and E3. �E1�, �E2� and �E3� are true. ____________________________ H is supported! Hypothetico-Deductive Method Lars-G�ran Johansson 16

17. Hypothetico-Deductive Method Formulate a hypothesis Deduce empirical consquences from the hypothesis and auxiliary assumptions. Compare these consequences with empirical data Form a conclusion: is the hypothesis falsified or supported by evidence? Hypothetico-Deductive Method Lars-G�ran Johansson 17

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21. General conclusions: 1.One can never give a conclusive proof for an empirical hypothesis 2: One can never by purely logical means decide which of the hypotheses, auxiliary assumptions or observation reports are false, if one has an inconsistency. (Duhem-Quine-thesis) Hypothetico-Deductive Method Lars-G�ran Johansson 21

22. Definitions Hypothesis =def A statement such that we are not convinced about its truth ii) we use it as premise in a deduction of empirical consequences. Empirical Consequence =def.A statement such that i) follows from the hypothesis and auxiliary assumptions ii) under appropriate conditions can be decided by observations. Auxiliary assumption =def. A statement such that i) it is necessary for deducing an empirical consequence from a hypothesis ii) it is in the given situation not tested but taken to be true. Hypothetico-Deductive Method Lars-G�ran Johansson 22

23. Ad hoc-hypothesis Ad hoc-hypothesis = def. An assumption which is introduced solely for the purpose of saving an othervise refuted theory, and It does not simplify the theory or enables any new predictions. Hypothetico-Deductive Method Lars-G�ran Johansson 23

24. The geocentric system Hypothetico-Deductive Method Lars-G�ran Johansson 24

25. Complete eclipse Ringformed eclipse Hypothetico-Deductive Method Lars-G�ran Johansson 25

26. Statistical hypothesis testing Formulate an hypothesis H concering a property in a population H0 (the zero hypothesis) is the negation of H, i.e., P(H)+P(H0)=1 Determine your signifikance level: 0.05, 0.01 or 0.001 Draw a sample of n objects from the population and observe the frequency of the property Calculate the probability, given H0, for the observed frequency, or better, in the sample. If this probability is higher that the chosen significance, reject H. Hypothetico-Deductive Method Lars-G�ran Johansson 26

27. An example Suppose we have a new drug that might cure a lethal disease 18 patients with this disease are randomly chosen. They are randomly divided in a test group that is given the drug and a control group that is given placebo After some time the following outcome is observed: Hypothetico-Deductive Method Lars-G�ran Johansson 27

28. Outcome Hypothetico-Deductive Method Lars-G�ran Johansson 28

29. Calculation Question: What is the probability to get this outcome, assuming the zero hypthesis, i.e., that the drug has no effect? In how many ways can we sort 7 dead and 11 alive persons in two groups each consisting of 9 individuals? (23540) How many of these groups are such that 6 alive and 3 dead is in the first group? (385) Hence, P(O|H0)= 385/23540�0,016 Hypothetico-Deductive Method Lars-G�ran Johansson 29

30. Conclusion P(O|H0)�0,016 and P(O|H)�0,98 Hence, if we have chosen the significance level to be 5%, we should reject the zero-hypothesis and accept the test hypothesis. This is no proof of the test hypothesis! Nor can we know the probability for the test hypothesis, given the evidence: for P(H|O) ? P(O|H) Hypothetico-Deductive Method Lars-G�ran Johansson 30

31. Alternative method: Bayesianism Instead of chosing a significance level, we can start by assuming an a priori probability for the hypothesis. This a priori hypothesis is a mere guess! Using this as input in Bayes theorem, we can calculate the posterior probability for the hypothesis after the test results are obtained. The process can be repeated, if there is enough money. If two researchers use different priors, they will rapidly converge in their posterior probabilities! Hypothetico-Deductive Method Lars-G�ran Johansson 31

32. Bayes� theorem H0 is the zero hypothesisH is the test hypothesis U is the outcome of testP(H) is the prior P(U|H) is the likelihood Hypothetico-Deductive Method Lars-G�ran Johansson 32

33. Holism �The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occacions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Reevaluation of some statements entails reevaluation of others, because of their logical interconnections.� Hypothetico-Deductive Method Lars-G�ran Johansson 33

34. Continued �The total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to reevaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole.� W.V.O. Quine: Two Dogmas of Empiricism. Hypothetico-Deductive Method Lars-G�ran Johansson 34

35. Conclusion Whatever the details of the method, the conclusion drawn does not follow logically HDM is inductive reasoning! The conclusion is never completely certain; revision is in principle always possible Logical relations between hypotheses, auxiliary assumptions and empirical statements make for holism! Hypothetico-Deductive Method Lars-G�ran Johansson 35